Diophantine inequalities over Piatetski-Shapiro primes

被引：1
|
作者：
Huang, Jing [1 ]
Zhai, Wenguang [2 ]
Zhang, Deyu [1 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China
[2] China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China
来源：
FRONTIERS OF MATHEMATICS IN CHINA | 2021年 / 16卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Diophantine inequalities; Piatetski-Shapiro primes; exponential sums; additive problems; NUMBER; APPROXIMATION;
D O I：
10.1007/s11464-021-0916-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let c > 1 and 0 < gamma < 1. We study the solubility of the Diophantine inequality divide p1(c) + p2(c) + horizontal ellipsis + ps(c)- N divide < (log N)(- 1) in Piatetski-Shapiro primes p(1), p(2), horizontal ellipsis , p(s) of the form p(j) = [m(1/gamma)] for some m is an element of N, and improve the previous results in the cases s = 2, 3, 4.
引用
收藏
页码：749 / 770
页数：22
相关论文
共 50 条
  • [1] Diophantine inequalities over Piatetski-Shapiro primes
    Jing Huang
    Wenguang Zhai
    Deyu Zhang
    Frontiers of Mathematics in China, 2021, 16 : 749 - 770
  • [2] Diophantine approximation over Piatetski-Shapiro primes
    Li, Taiyu
    Liu, Huafeng
    JOURNAL OF NUMBER THEORY, 2020, 211 : 184 - 198
  • [3] Diophantine approximation by Piatetski-Shapiro primes
    Dimitrov, S. I.
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2022, 53 (04): : 875 - 883
  • [4] Diophantine approximation by Piatetski-Shapiro primes
    S. I. Dimitrov
    Indian Journal of Pure and Applied Mathematics, 2022, 53 : 875 - 883
  • [5] An additive problem over Piatetski-Shapiro primes and almost-primes
    Li, Jinjiang
    Zhang, Min
    Xue, Fei
    RAMANUJAN JOURNAL, 2022, 57 (04): : 1307 - 1333
  • [6] An additive problem on Piatetski-Shapiro primes
    Ya Ming Lu
    Acta Mathematica Sinica, English Series, 2018, 34 : 255 - 264
  • [7] Piatetski-Shapiro primes from almost primes
    Roger C. Baker
    William D. Banks
    Zhenyu V. Guo
    Aaron M. Yeager
    Monatshefte für Mathematik, 2014, 174 : 357 - 370
  • [8] Piatetski-Shapiro primes from almost primes
    Baker, Roger C.
    Banks, William D.
    Guo, Zhenyu V.
    Yeager, Aaron M.
    MONATSHEFTE FUR MATHEMATIK, 2014, 174 (03): : 357 - 370
  • [9] Almost primes in Piatetski-Shapiro sequences
    Guo, Victor Zhenyu
    AIMS MATHEMATICS, 2021, 6 (09): : 9536 - 9546
  • [10] On the distribution of αp modulo one over Piatetski-Shapiro primes
    Dimitrov, Stoyan
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023, 54 (03): : 858 - 867
12345